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Merge #31880
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@mkoeppe
mkoeppe committed Jun 19, 2021
2 parents 46eed0e + 8abdc8b commit 5b0f85d
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9 changes: 5 additions & 4 deletions src/sage/functions/piecewise.py
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Original file line number Diff line number Diff line change
@@ -1,3 +1,4 @@
# -*- coding: utf-8 -*-
r"""
Piecewise-defined Functions
Expand Down Expand Up @@ -527,7 +528,7 @@ def restriction(self, parameters, variable, restricted_domain):
sage: f = piecewise([((-oo, oo), x)]); f
piecewise(x|-->x on (-oo, +oo); x)
sage: f.restriction([[-1,1], [3,3]])
piecewise(x|-->x on [-1, 1] + {3}; x)
piecewise(x|-->x on [-1, 1] ∪ {3}; x)
"""
restricted_domain = RealSet(*restricted_domain)
new_param = []
Expand Down Expand Up @@ -559,7 +560,7 @@ def extension(self, parameters, variable, extension, extension_domain=None):
ValueError: point 3 is not in the domain
sage: g = f.extension(0); g
piecewise(x|-->x on (-1, 1), x|-->0 on (-oo, -1] + [1, +oo); x)
piecewise(x|-->x on (-1, 1), x|-->0 on (-oo, -1] ∪ [1, +oo); x)
sage: g(3)
0
Expand All @@ -583,7 +584,7 @@ def unextend_zero(self, parameters, variable):
sage: f = piecewise([((-1,1), x)]); f
piecewise(x|-->x on (-1, 1); x)
sage: g = f.extension(0); g
piecewise(x|-->x on (-1, 1), x|-->0 on (-oo, -1] + [1, +oo); x)
piecewise(x|-->x on (-1, 1), x|-->0 on (-oo, -1] ∪ [1, +oo); x)
sage: g(3)
0
sage: h = g.unextend_zero()
Expand Down Expand Up @@ -652,7 +653,7 @@ def piecewise_add(self, parameters, variable, other):
sage: f = piecewise([([0,1], 1), ((2,3), x)])
sage: g = piecewise([((1/2, 2), x)])
sage: f.piecewise_add(g).unextend_zero()
piecewise(x|-->1 on (0, 1/2], x|-->x + 1 on (1/2, 1], x|-->x on (1, 2) + (2, 3); x)
piecewise(x|-->1 on (0, 1/2], x|-->x + 1 on (1/2, 1], x|-->x on (1, 2) ∪ (2, 3); x)
"""
points = ([minus_infinity] +
sorted(set(self.end_points() + other.end_points())) +
Expand Down
125 changes: 82 additions & 43 deletions src/sage/sets/real_set.py
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Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,7 @@
sage: RealSet(0,1)
(0, 1)
sage: RealSet((0,1), [2,3])
(0, 1) + [2, 3]
(0, 1) ∪ [2, 3]
sage: RealSet(-oo, oo)
(-oo, +oo)
Expand Down Expand Up @@ -42,7 +42,7 @@
Relations containing symbols and numeric values or constants::
sage: RealSet(x != 0)
(-oo, 0) + (0, +oo)
(-oo, 0) ∪ (0, +oo)
sage: RealSet(x == pi)
{pi}
sage: RealSet(x < 1/2)
Expand Down Expand Up @@ -382,6 +382,31 @@ def _repr_(self):
s += ']' if self._upper_closed else ')'
return s

def _latex_(self):
"""
Return a latex representation of ``self``.
EXAMPLES::
sage: RealSet.open_closed(1/2, pi)._latex_()
'(\\frac{1}{2}, \\pi]'
sage: (RealSet.point(sqrt(2)))._latex_()
'\\{\\sqrt{2}\\}'
"""
from sage.misc.latex import latex
if self.is_point():
# Converting to str avoids the extra whitespace
# that LatexExpr add on concenation. We do not need
# the whitespace because we are wrapping it in
# non-letter characters.
return r'\{' + str(latex(self.lower())) + r'\}'
s = '[' if self._lower_closed else '('
s += str(latex(self.lower()))
s += ', '
s += str(latex(self.upper()))
s += ']' if self._upper_closed else ')'
return s

def _sympy_condition_(self, variable):
"""
Convert to a sympy conditional expression.
Expand Down Expand Up @@ -742,12 +767,12 @@ def __classcall__(cls, *args):
EXAMPLES::
sage: R = RealSet(RealSet.open_closed(0,1), RealSet.closed_open(2,3)); R
(0, 1] + [2, 3)
(0, 1] ∪ [2, 3)
::
sage: RealSet(x != 0)
(-oo, 0) + (0, +oo)
(-oo, 0) ∪ (0, +oo)
sage: RealSet(x == pi)
{pi}
sage: RealSet(x < 1/2)
Expand Down Expand Up @@ -882,9 +907,9 @@ def __init__(self, *intervals):
sage: RealSet(i) # interval
(0, 1)
sage: RealSet(i, (3,4)) # tuple of two numbers = open set
(0, 1) + (3, 4)
(0, 1) ∪ (3, 4)
sage: RealSet(i, [3,4]) # list of two numbers = closed set
(0, 1) + [3, 4]
(0, 1) ∪ [3, 4]
Real sets belong to a subcategory of topological spaces::
Expand Down Expand Up @@ -1128,9 +1153,9 @@ def normalize(intervals):
sage: RealSet((0, 1), [1, 2], (2, 3))
(0, 3)
sage: RealSet((0, 1), (1, 2), (2, 3))
(0, 1) + (1, 2) + (2, 3)
(0, 1) ∪ (1, 2) ∪ (2, 3)
sage: RealSet([0, 1], [2, 3])
[0, 1] + [2, 3]
[0, 1] ∪ [2, 3]
sage: RealSet((0, 2), (1, 3))
(0, 3)
sage: RealSet(0,0)
Expand Down Expand Up @@ -1158,7 +1183,7 @@ def normalize(intervals):

def _repr_(self):
"""
Return a string representation
Return a string representation of ``self``.
OUTPUT:
Expand All @@ -1172,10 +1197,24 @@ def _repr_(self):
if self.n_components() == 0:
return '{}'
else:
# Switch to u'\u222A' (cup sign) with Python 3
return ' + '.join(map(repr, self._intervals))
# return u' ∪ '.join(map(repr, self._intervals)) # py3 only
return ' ∪ '.join(map(repr, self._intervals))

def _latex_(self):
r"""
Return a latex representation of ``self``.
EXAMPLES::
sage: latex(RealSet(0, 1))
(0, 1)
sage: latex((RealSet(0, 1).union(RealSet.unbounded_above_closed(2))))
(0, 1) \cup [2, +\infty)
"""
from sage.misc.latex import latex
if self.n_components() == 0:
return r'\emptyset'
else:
return r' \cup '.join(latex(i) for i in self._intervals)

def _sympy_condition_(self, variable):
"""
Expand Down Expand Up @@ -1492,26 +1531,26 @@ def intersection(self, *other):
EXAMPLES::
sage: s1 = RealSet(0,2) + RealSet.unbounded_above_closed(10); s1
(0, 2) + [10, +oo)
(0, 2) ∪ [10, +oo)
sage: s2 = RealSet(1,3) + RealSet.unbounded_below_closed(-10); s2
(-oo, -10] + (1, 3)
(-oo, -10] ∪ (1, 3)
sage: s1.intersection(s2)
(1, 2)
sage: s1 & s2 # syntactic sugar
(1, 2)
sage: s1 = RealSet((0, 1), (2, 3)); s1
(0, 1) + (2, 3)
(0, 1) ∪ (2, 3)
sage: s2 = RealSet([0, 1], [2, 3]); s2
[0, 1] + [2, 3]
[0, 1] ∪ [2, 3]
sage: s3 = RealSet([1, 2]); s3
[1, 2]
sage: s1.intersection(s2)
(0, 1) + (2, 3)
(0, 1) ∪ (2, 3)
sage: s1.intersection(s3)
{}
sage: s2.intersection(s3)
{1} + {2}
{1} ∪ {2}
"""
other = RealSet(*other)
# TODO: this can be done in linear time since the intervals are already sorted
Expand All @@ -1534,12 +1573,12 @@ def inf(self):
EXAMPLES::
sage: s1 = RealSet(0,2) + RealSet.unbounded_above_closed(10); s1
(0, 2) + [10, +oo)
(0, 2) ∪ [10, +oo)
sage: s1.inf()
0
sage: s2 = RealSet(1,3) + RealSet.unbounded_below_closed(-10); s2
(-oo, -10] + (1, 3)
(-oo, -10] ∪ (1, 3)
sage: s2.inf()
-Infinity
"""
Expand All @@ -1558,12 +1597,12 @@ def sup(self):
EXAMPLES::
sage: s1 = RealSet(0,2) + RealSet.unbounded_above_closed(10); s1
(0, 2) + [10, +oo)
(0, 2) ∪ [10, +oo)
sage: s1.sup()
+Infinity
sage: s2 = RealSet(1,3) + RealSet.unbounded_below_closed(-10); s2
(-oo, -10] + (1, 3)
(-oo, -10] ∪ (1, 3)
sage: s2.sup()
3
"""
Expand All @@ -1582,17 +1621,17 @@ def complement(self):
EXAMPLES::
sage: RealSet(0,1).complement()
(-oo, 0] + [1, +oo)
(-oo, 0] ∪ [1, +oo)
sage: s1 = RealSet(0,2) + RealSet.unbounded_above_closed(10); s1
(0, 2) + [10, +oo)
(0, 2) ∪ [10, +oo)
sage: s1.complement()
(-oo, 0] + [2, 10)
(-oo, 0] ∪ [2, 10)
sage: s2 = RealSet(1,3) + RealSet.unbounded_below_closed(-10); s2
(-oo, -10] + (1, 3)
(-oo, -10] ∪ (1, 3)
sage: s2.complement()
(-10, 1] + [3, +oo)
(-10, 1] ∪ [3, +oo)
"""
n = self.n_components()
if n == 0:
Expand Down Expand Up @@ -1630,19 +1669,19 @@ def difference(self, *other):
EXAMPLES::
sage: s1 = RealSet(0,2) + RealSet.unbounded_above_closed(10); s1
(0, 2) + [10, +oo)
(0, 2) ∪ [10, +oo)
sage: s2 = RealSet(1,3) + RealSet.unbounded_below_closed(-10); s2
(-oo, -10] + (1, 3)
(-oo, -10] ∪ (1, 3)
sage: s1.difference(s2)
(0, 1] + [10, +oo)
(0, 1] ∪ [10, +oo)
sage: s1 - s2 # syntactic sugar
(0, 1] + [10, +oo)
(0, 1] ∪ [10, +oo)
sage: s2.difference(s1)
(-oo, -10] + [2, 3)
(-oo, -10] ∪ [2, 3)
sage: s2 - s1 # syntactic sugar
(-oo, -10] + [2, 3)
(-oo, -10] ∪ [2, 3)
sage: s1.difference(1,11)
(0, 1] + [11, +oo)
(0, 1] ∪ [11, +oo)
"""
other = RealSet(*other)
return self.intersection(other.complement())
Expand All @@ -1664,7 +1703,7 @@ def contains(self, x):
EXAMPLES::
sage: s = RealSet(0,2) + RealSet.unbounded_above_closed(10); s
(0, 2) + [10, +oo)
(0, 2) ∪ [10, +oo)
sage: s.contains(1)
True
sage: s.contains(0)
Expand Down Expand Up @@ -1758,7 +1797,7 @@ def is_disjoint_from(self, *other):
EXAMPLES::
sage: s1 = RealSet((0, 1), (2, 3)); s1
(0, 1) + (2, 3)
(0, 1) ∪ (2, 3)
sage: s2 = RealSet([1, 2]); s2
[1, 2]
sage: s1.is_disjoint_from(s2)
Expand Down Expand Up @@ -1863,15 +1902,15 @@ def __mul__(self, right):
EXAMPLES::
sage: A = RealSet([0, 1/2], (2, infinity)); A
[0, 1/2] + (2, +oo)
[0, 1/2] ∪ (2, +oo)
sage: 2 * A
[0, 1] + (4, +oo)
[0, 1] ∪ (4, +oo)
sage: A * 100
[0, 50] + (200, +oo)
[0, 50] ∪ (200, +oo)
sage: 1.5 * A
[0.000000000000000, 0.750000000000000] + (3.00000000000000, +oo)
[0.000000000000000, 0.750000000000000] ∪ (3.00000000000000, +oo)
sage: (-2) * A
(-oo, -4) + [-1, 0]
(-oo, -4) ∪ [-1, 0]
"""
if not isinstance(right, RealSet):
return RealSet(*[e * right for e in self])
Expand All @@ -1887,8 +1926,8 @@ def __rmul__(self, other):
TESTS::
sage: A = RealSet([0, 1/2], RealSet.unbounded_above_closed(2)); A
[0, 1/2] + [2, +oo)
[0, 1/2] ∪ [2, +oo)
sage: pi * A
[0, 1/2*pi] + [2*pi, +oo)
[0, 1/2*pi] ∪ [2*pi, +oo)
"""
return self * other

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